SOLUTION: Hello iam currently taking a college algebra class and my professor gave me this bonus problem y=log9(log 8(log 7(log 6(log 5(x)))))) and find the domain of dy/dx. i have no idea w

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hello iam currently taking a college algebra class and my professor gave me this bonus problem y=log9(log 8(log 7(log 6(log 5(x)))))) and find the domain of dy/dx. i have no idea w      Log On


   

Question 606592: Hello iam currently taking a college algebra class and my professor gave me this bonus problem y=log9(log 8(log 7(log 6(log 5(x)))))) and find the domain of dy/dx. i have no idea where or how to begin this problem any help is appreciated.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!


First, we should find where x is defined. Note that the domain of any log function is always the positive real numbers (unless we are dealing with complex logarithms -- which we are not).

Hence,





(see the pattern?)





Therefore any value of x such that is in the domain. Since log x is a differentiable function, log(log(x)) is differentiable, and so on. The domain of dy/dx is the same as the domain of y.